Abstract
The origin of the present paper is the desire to study the asymptotic behaviour of certain tests of significance which can be based on maximum-likelihood estimators. The standard theory of such problems (e.g. Wald(4)) assumes, sometimes tacitly, that the parameter point corresponding to the null hypothesis lies inside an open set in the parameter space. Here we wish to study what happens when the true parameter point, in estimation problems, lies on the boundary of the parameter space.
Keywords
Parameter spaceEstimatorMathematicsMaximum likelihoodEstimation theoryNull hypothesisPoint (geometry)Point estimationSpace (punctuation)Score testBoundary (topology)Applied mathematicsNull (SQL)Wald testRestricted maximum likelihoodSet (abstract data type)StatisticsStatistical hypothesis testingMathematical analysisComputer scienceGeometry
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Publication Info
- Year
- 1971
- Type
- article
- Volume
- 70
- Issue
- 3
- Pages
- 441-450
- Citations
- 172
- Access
- Closed
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Cite This
P. A. P. Moran
(1971).
Maximum-likelihood estimation in non-standard conditions.
Mathematical Proceedings of the Cambridge Philosophical Society
, 70
(3)
, 441-450.
https://doi.org/10.1017/s0305004100050088
Identifiers
- DOI
- 10.1017/s0305004100050088